A Modified of Fourth-Order Partial Differential Equations Model Based on Isophote Direction to Noise Image Removal
DOI:
https://doi.org/10.32792/jeps.v14i3.442الكلمات المفتاحية:
Image denoising، Fourth-order partial differential equations، nonlinear filtering، isophote direction، finite difference methodالملخص
Image denoising is one of the initial stages of image processing. Many models based on the diffusion method have been used to smooth the image. One of the problems, we face in the model based on the diffusion method is its possible loss of edges. The diffusion force is known to be more effective in areas of high frequency. So This paper suggests combining the direction of isophote and fourth-order partial differential equations to reduce the problem of loss edges and preserve important details of the image. The direction of the isophote can regulate the direction of diffusion. Thus, we have a proposed model that can remove the noise in the area while preserving the important edges and details of the image. We have proven the efficiency and superiority of the proposed model by applying it to a set of images and solving it numerically using the finite difference method (FDM).
المراجع
[ 1] Al‐Griffi, T. A. J., & Al‐Saif, A. S. J. (2022). Yang transform–homotopy perturbation method for solving a non‐Newtonian viscoelastic fluid flow on the turbine disk. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 102(8), e202100116.
[ 2] Abdul-Ameer, Y. A., & Ali Al-Saif, A. S. J. (2023). Fourier-homotopy perturbation method for heat and mass transfer with 2D unsteady squeezing viscous flow problem. Journal of Computational Applied Mechanics, 54(2), 219-235.
[ 3] Al–Sadi, R. O., & Al-Saif, A. S. J. (2023). Development and simulation of a mathematical model representing the dynamics of type 1 diabetes mellitus with treatment. Partial Differential Equations in Applied Mathematics, 8, 100575.
[ 4] Chan, T. F., & Esedoglu, S. (2005). Aspects of total variation regularized L 1 function approximation. SIAM Journal on Applied Mathematics, 65(5), 1817-1837.
[ 5] Strong, D., & Chan, T. (2003). Edge-preserving and scale-dependent properties of total variation regularization. Inverse problems, 19(6), S165.
[ 6] koenderink, J. J. (1984). The structure of images. Biological cybernetics, 50(5), 363-370
[ 7] Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on pattern analysis and machine intelligence, 12(7), 629-639
[ 8] You, Y. L., & Kaveh, M. (2000). Fourth-order partial differential equations for noise removal. IEEE Transactions on Image Processing, 9(10), 1723-1730
[ 9] Vanitha, K., Satyanarayana, D., & Prasad, M. G. (2019, July). A new hybrid medical image fusion method based on fourth-order partial differential equations decomposition and DCT in SWT domain. In 2019 10th International Conference on Computing, Communication and Networking Technologies (ICCCNT) (pp. 1-6). IEEE.
[ 10] Wang, Y., Ji, X., & Dai, Q. (2010). Fourth-order oriented partial-differential equations for noise removal of two-photon fluorescence images. Optics letters, 35(17), 2943-2945
[ 11] Yadava, P. C., & Srivastava, S. (2024). Denoising of Poisson-corrupted microscopic biopsy images using a fourth-order partial differential equation with ant colony optimization. Biomedical Signal Processing and Control, 93, 106207
[ 12] Bavirisetti, D. P., Xiao, G., & Liu, G. (2017, July). Multi-sensor image fusion based on fourth-order partial differential equations. In 2017 20th International Conference on Information Fusion (Fusion) (pp. 1-9). IEEE
[ 13] Calatroni, L., Düring, B., & Schönlieb, C. B. (2013). ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. arXiv preprint arXiv:1305.5362
[ 14] Laghrib, A., Chakib, A., Hadri, A., & Hakim, A. (2020). A nonlinear fourth-order PDE for multi-frame image super-resolution enhancement. Discrete & Continuous Dynamical Systems-B, 25(1), 415
[ 15] Lysaker, M., Lundervold, A., & Tai, X. C. (2003). Noise removal using a fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Transactions on image processing, 12(12), 1579-1590
[ 16] Ying, W., Jiebao, S., & Zhichang, G. (2022). A new anisotropic fourth-order diffusion equation model based on image features for image denoising. Inverse Problems and Imaging, 16(4), 895-924
[ 17] Khoeiniha, N., Hosseini, S. M., & Davoudi, R. (2021). Trainable fourth-order partial differential equations for image noise removal. Iranian Journal of Numerical Analysis and Optimization, 11(2), 235-260
[ 18] Liu, X. Y., Lai, C. H., & Pericleous, K. A. (2015). A fourth-order partial differential equation denoising model with an adaptive relaxation method. International Journal of Computer Mathematics, 92(3), 608-622
[ 19] Kim, J. B., & Kim, H. J. (2003). GA-based image restoration by isophote constraint optimization. EURASIP Journal on Advances in Signal Processing, 2003, 1-6
[ 20] Sun, X., & Xu, C. (2009, December). Image denoising and inpainting model based on Taylor expansion. In 2009 International Conference on Computational Intelligence and Security (Vol. 1, pp. 666-670). IEEE
[ 21] C. F. and D. M. Pablo Arbelaez, “The Berkeley Segmentation Dataset and Benchmark,” 2007. The website of the Berkeley database is https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/
[ 22] Bovik, A. C. (2010). Handbook of image and video processing. Academic press
[ 23] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4), 600-612
[ 24] Gu, K., Wang, S., Zhai, G., Lin, W., Yang, X., & Zhang, W. (2016). Analysis of distortion distribution for pooling in image quality prediction. IEEE Transactions on Broadcasting, 62(2), 446-456
[ 25] Rodrigues, I., Sanches, J., & Bioucas-Dias, J. (2008, October). Denoising of medical images corrupted by Poisson noise. In 2008 15th IEEE International Conference on Image Processing, pp. 1756-1759.
[ 26] Liang, H., Li, N., & Zhao, S. (2021). Salt and pepper noise removal method based on a detail-aware filter. Symmetry, 13(3), 515.
[ 27] Chan, R. H., Ho, C. W., & Nikolova, M. (2005). Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization. IEEE Transactions on Image Processing, 14(10), 1479-1485.
[ 28] Maity, A., Pattanaik, A., Sagnika, S., & Pani, S. (2015, January). A comparative study on approaches to speckle noise reduction in images. In 2015 International Conference on Computational Intelligence and Networks (pp. 148-155). IEEE.
[ 29] Jaybhay, J., & Shastri, R. (2015). A study of speckle noise reduction filters. signal & image processing: An international Journal (SIPIJ), 6(3), 71
التنزيلات
منشور
إصدار
القسم
الرخصة
الحقوق الفكرية (c) 2024 Journal of Education for Pure Science- University of Thi-Qar
هذا العمل مرخص بموجب Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The Authors understand that, the copyright of the articles shall be assigned to Journal of education for Pure Science (JEPS), University of Thi-Qar as publisher of the journal.
Copyright encompasses exclusive rights to reproduce and deliver the article in all form and media, including reprints, photographs, microfilms and any other similar reproductions, as well as translations. The reproduction of any part of this journal, its storage in databases and its transmission by any form or media, such as electronic, electrostatic and mechanical copies, photocopies, recordings, magnetic media, etc. , will be allowed only with a written permission from Journal of education for Pure Science (JEPS), University of Thi-Qar.
Journal of education for Pure Science (JEPS), University of Thi-Qar, the Editors and the Advisory International Editorial Board make every effort to ensure that no wrong or misleading data, opinions or statements be published in the journal. In any way, the contents of the articles and advertisements published in the Journal of education for Pure Science (JEPS), University of Thi-Qar are sole and exclusive responsibility of their respective authors and advertisers.
